Convex ENO high order multi-dimensional schemes without field by field decomposition or staggered grids
type: Item
instance of: scholarly article
title: Convex ENO high order multi-dimensional schemes without field by field decomposition or staggered grids
zbMATH Open document ID: 0941.65082
author: Xu-Dong Liu
author: Stanley Osher
published in: Journal of Computational Physics
publication date: 2000-07-20T00:00:00Z
review text: The main purpose of the paper is the presentation of a new central essentially nonoscillatory (ENO) scheme, which is of third order and does not require field-by-field decomposition. First, the standard ENO schemes developed by \textit{C.-W. Shu} and \textit{S. Osher} [J. Comput. Phys. 83, No.~1, 32-78 (1989; Zbl 0674.65061)] are revisited by using point values instead of cell averages, which avoids staggering, as well as component-wise limiting. Next the authors introduce a new type of decision process called ``convex ENO'', which yields the desired scheme. They insist on the fact that their flux does degenerate to first order at discontinuities. Furthermore, their scheme is easily extended to multi-dimensions. Numerical results are reported in detail for 10 significant test problems in one or two dimensions. They are excellent. It is also pointed out that the component-wise calculation is twice as fast as the field-by-field decomposition version of the scheme in each dimension.
Mathematics Subject Classification ID: 65M06
Mathematics Subject Classification ID: 65M12
Mathematics Subject Classification ID: 35L65
zbMATH DE Number: 1281849
zbMATH Keywords: central schemes
zbMATH Keywords: essentially nonoscillatory scheme
zbMATH Keywords: component-wise calculation
zbMATH Keywords: high resolution methods
zbMATH Keywords: multi-dimensions
zbMATH Keywords: numerical results
zbMATH Keywords: ENO scheme
MaRDI profile type: Publication
full work available at URL: jcph.1998.5937
OpenAlex ID: W2086936948
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DOI: 10.1006/JCPH.1998.5937
description: scientific article; zbMATH DE number 1281849